Iec 60076-12-2008.Pdf

IEC 60076 12 Edition 1 0 2008 11 INTERNATIONAL STANDARD NORME INTERNATIONALE Power transformers – Part 12 Loading guide for dry type power transformers Transformateurs de puissance – Partie 12 Guide d[.]

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CONTENTS

FOREWORD 4

INTRODUCTION 6

1 Scope 7

2 Normative references 7

3 Terms and definitions 7

4 Effect of loading beyond nameplate rating 8

4.1 General 8

4.2 General consequences 8

4.3 Effects and hazards of short-time emergency loading 8

4.4 Effects of long-time emergency loading 9

5 Ageing and transformer insulation lifetime 9

5.1 General 9

5.2 Lifetime 9

5.3 Relation between constant continuous load and temperature 10

5.4 Ageing rate 11

5.5 Lifetime consumption 11

5.6 Hot-spot temperature in steady state 11

5.7 Assumed hot-spot factor 12

5.8 Hot-spot temperature rises at varying ambient temperature and load conditions 12

5.9 Loading equations 12

5.9.1 Continuous loading 12

5.9.2 Transient loading 13

5.10 Determination of winding time constant 14

5.10.1 General 14

5.10.2 Time constant calculation method 14

5.10.3 Time constant test method 15

5.11 Determination of winding time constant according to empirical constant 15

5.12 Calculation of loading capability 15

6 Limitations 17

6.1 Current and temperature limitations 17

6.2 Other limitations 17

6.2.1 Magnetic leakage field in structural metallic parts 17

6.2.2 Accessories and other considerations 17

6.2.3 Transformers in an enclosure 18

6.2.4 Outdoor ambient conditions 18

Annex A (informative) Ageing rate 19

Annex B (informative) Examples of lifetime consumptions for 3 load regimes 24

Annex C (informative) List of symbols 33

Bibliography 35

Figure A.1 – Molecule structure of an epoxy 19

Figure A.2 – Thermal endurance graph 22

Figure B.1 – Step change loading curve 25

Figure B.2 – Hot-spot temperature rise and life consumption 27

Figure B.3 – Load current and winding hot-spot temperature rise 30

Figure B.4 – Ageing rate versus time 30

Table 1 – Constants for lifetime equation 10

Table 2 – Maximum hot-spot winding temperature 16

Table 3 – Current and temperature limits applicable to loading beyond nameplate rating 17

Table B.1 – Lifetime consumption calculations 26

Table B.2 – Life consumption calculations for varying load 29

Table B.3 – Life consumption calculation 31

INTERNATIONAL ELECTROTECHNICAL COMMISSION

POWER TRANSFORMERS – Part 12: Loading guide for dry-type power transformers

FOREWORD

1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising

all national electrotechnical committees (IEC National Committees) The object of IEC is to promote

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indispensable for the correct application of this publication

9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of

patent rights IEC shall not be held responsible for identifying any or all such patent rights

International Standard IEC 60076-12 has been prepared by IEC technical committee 14:

Power transformers

This standards cancels and replaces IEC 60905 (1987) This first edition constitutes a

technical revision

The text of this standard is based on the following documents:

FDIS Report on voting 14/584/FDIS 14/590/RVD

Full information on the voting for the approval of this standard can be found in the report on

voting indicated in the above table

This publication has been drafted in accordance with the ISO/IEC Directives, Part 2

A list of all parts of IEC 60076 series, under the general title Power transformers, can be

found on the IEC website

The committee has decided that the contents of this publication will remain unchanged until

the maintenance result date indicated on the IEC web site under "http://webstore.iec.ch" in

the data related to the specific publication At this date, the publication will be

• reconfirmed;

• withdrawn:

• replaced by a revised edition; or

• amended

INTRODUCTION

This part of IEC 60076 provides guidance for the specification and loading of dry type power

transformers from the point of view of operating temperatures and thermal ageing It provides

the consequence of loading above the nameplate rating and guidance for the planner to

choose appropriate rated quantities and loading conditions for new installations

IEC 60076-11 is the basis for contractual agreements and it contains the requirements and

tests relating to temperature-rise figures for dry type power transformers during continuous

rated loading It should be noted that IEC 60076-11 refers to the average winding temperature

rise while this part of IEC 60076 refers mainly to the hot-spot temperature and the latter

stated values are provided only for guidance

This part of IEC 60076 gives mathematical models for judging the consequence of different

loading, with different temperatures of the cooling medium, and with transient or cyclical

variation with time The models provide for the calculation of operating temperatures in the

transformer, particularly the temperature of the hottest part of the winding This hot-spot

temperature is used for estimation of the number of hours of life time consumed during a

particular time period

This part of IEC 60076 further presents recommendations for limitations of permissible

loading according to the results of temperature calculations or measurements These

recommendations refer to different types of loading duty – continuous loading, short-time and

long time emergency loading An explanation of ageing fundamentals is given in Annex A

POWER TRANSFORMERS – Part 12: Loading guide for dry-type power transformers

1 Scope

This part of IEC 60076 is applicable to dry-type transformers according to the scope of

IEC 60076-11 It provides the means to estimate ageing rate and consumption of lifetime of

the transformer insulation as a function of the operating temperature, time and the loading of

the transformer

NOTE For special applications such as wind turbine application transformers, furnace transformers, welding

machine transformers, and others, the manufacturer should be consulted regarding the particular loading profile

2 Normative references

The following referenced documents are indispensable for the application of this document

For dated references, only the edition cited applies For undated references, the latest edition

of the referenced document (including any amendments) applies

IEC 60076-11, Power transformers – Part 11: Dry-type transformers

IEC 60216-1, Electrical insulating materials – Properties of thermal endurance –

Part 1: Ageing procedures and evaluation of test results

IEC 61378-1:1997, Convertor transformers – Part 1: Transformers for industrial applications

3 Terms and definitions

For the purposes of this document, the following terms and definitions apply

3.1

long-time emergency loading

loading resulting from the prolonged outage of some system elements that will not be

reconnected before the transformer reaches a new and higher steady state temperature

3.2

short-time emergency loading

unusually heavy loading of a transient nature (less than one time constant of the coil) due to

the occurrence of one or more unlikely events which seriously disturb normal system loading

3.3

hot-spot

if not specifically defined, “hot-spot” means the hottest-spot of the winding

3.4

relative thermal ageing rate

for a given hot-spot temperature, the rate at which transformer insulation ageing is reduced or

accelerated compared with the ageing rate at a reference hot-spot temperature

3.5

transformer insulation life time

the total time between the initial state for which the normal transformer insulation life time is

considered new and the final state when due to thermal ageing, dielectric stress, short-circuit

stress, or mechanical movement, which could occur in normal service and result in a high risk

method of cooling to increase the rated power of the transformer with fan cooling

4 Effect of loading beyond nameplate rating

4.1 General

Normal life expectancy is a conventional reference basis for continuous duty under design

ambient temperature and rated operating conditions The application of a load in excess of

nameplate rating and/or an ambient temperature higher than specified ambient temperatures

involves a degree of risk and accelerated ageing It is the purpose of this part of IEC 60076 to

identify such risks and to indicate how, within limitations, transformers may be loaded in

excess of the nameplate rating

The consequences of loading a transformer beyond its nameplate rating are as follows:

– the temperatures of windings, terminals, leads, tap changer and insulation increase, and

can reach unacceptable levels;

– enclosure cooling is more sensitive to overload leading to a more rapid increase in

insulation temperature to unacceptable levels;

– as a consequence, there will be a risk of premature failure associated with the increased

currents and temperatures This risk may be of an immediate short-term character or may

come from the cumulative effect of thermal ageing of the insulation in the transformer over

many years

NOTE Another consequence of overload is an increased voltage drop in the transformer

4.3 Effects and hazards of short-time emergency loading

The main risks, for short-time emergency loading over the specified limits, are

– critical mechanical stresses due to increased temperature, which can reach an

unacceptable level causing cracks in the insulation of a cast resin transformer;

– mechanical damage in the winding due to short and repetitive current above rated current;

– mechanical damage in the winding due to short and repetitive current combined with

ambient temperature higher than specified;

– deterioration of mechanical properties at higher temperature could reduce the short-circuit

strength;

– reduction of dielectric strength due to elevated temperature

As a result the maximum overcurrent is limited to 50 % over the rated nominal current

The agreement of the manufacturer is necessary in case of overloading in excess of 50 % to

assess the consequences of such overloading In any case the duration of such overloading

should be kept as short as possible

4.4 Effects of long-time emergency loading

The effects of long-time emergency loading are the following:

– cumulative thermal deterioration of the mechanical and dielectric properties of the

conductor insulation will accelerate at higher temperatures If this deterioration proceeds

far enough, it reduces the lifetime of the transformer, particularly if the apparatus is

subjected to system short-circuits;

– other insulation materials, as well as structural parts and the conductors, suffer increased

ageing rate at higher temperature;

– the calculation rules for ageing rate and consumption of lifetime are based on

considerations of loading

5 Ageing and transformer insulation lifetime

5.1 General

Experience indicates that the normal lifetime of a transformer is some tens of years It cannot

be stated more precisely, because it may vary even between identical units, owing in

particular to operating factors, which may differ from one transformer to another With few

exceptions a transformer rarely operates at 100 % of rated current throughout its lifetime

Other heating factors such as insufficient cooling, harmonics, over fluxing and/or unusual

conditions as described in 60076-11 could also affect the life of the transformer

When heat, which is mainly due to the transformer losses, is transferred to the insulation

system, a chemical process begins This process changes the molecular structure of the

materials which form the insulation system The ageing rate increases with the amount of heat

transferred to the system This process is cumulative and irreversible, which means that the

materials do not regain their original molecular structure when the heat supply stops and the

temperature decreases The thermal index of the insulation system is stated in the

manufacturer’s documentation and is also written on the rating plate It is assumed that failing

insulation due to ageing is one of the causes of end of lifetime of the transformer

Further it is assumed that the ageing rate varies with temperature according to the Arrhenius’

equation See Annex A for additional background information The two constants in Arrhenius’

equation should ideally be determined by means of thermal endurance testing In cases where

data from such testing is missing, this guide provides estimated constants, which are

calculated on the basis of the following assumptions:

– a temperature increase of 6 K doubles the ageing rate 6 K is an estimated value for the

whole winding linked with the value of specific materials used in the winding;

– another value for this doubling rate should be used when supported by thermal endurance

tests on the complete electrical insulation system (EIS), according to IEC 60216-1;

– insulation failures are the cause of end of life of the transformer

5.2 Lifetime

The expected lifetime L of a transformer at a constant hot-spot thermodynamic temperature T

in Kelvin (K) can be calculated by means of the equation:

T

b

e a

This equation can be written more conveniently as:

T

b a

Although any time unit may be used in these formulas, the hour is used in this guide The

constant a, given in Table 1 for the different insulation system temperatures, is based on this

time unit

NOTE 1 The expected lifetime calculated according to this equation should not be perceived in a too literal sense

The ability of the transformer to withstand high currents due to short-circuits in the power system and

over-voltages is, after this theoretically calculated lifetime, certainly weakened compared to a new transformer In the

absence of such disturbances the transformer may still operate satisfactorily for many years Taking precaution to

avoid short-circuit and installing adequate over-voltage protection may extend the transformer lifetime

Table 1 – Constants for lifetime equation

Arrhenius' equation constants

Insulation system temperature

Rated hot spot winding temperature

r HS,

000 180 ( ln

r HS,

a b

+ +

= ϑ

) ( ln 273 6 )

000 90 ( ln

r HS,

a b

+ + +

= ϑ

r

HS,

ϑ is the winding rated hot-spot temperature;

Ti is insulation system temperature (thermal index Ti)

The Table 1 is calculated by doubling the ageing for each 6 K.

NOTE 3 Most power transformers operate well below full load most of their actual lifetime Since a hot-spot

temperature of as little as 6 °C below rated values results in half the rated loss of life, the actual lifetime of a

transformer typically exceeds 20 years Accordingly, the constants in Table 1 were developed based on 180 000 h

using a halving constant of 6 K

5.3 Relation between constant continuous load and temperature

The constant hot-spot thermodynamic temperature T, in Kelvin (K), of the winding is given by:

HSn a

ϑ is the ambient temperature in degrees Celsius (°C);

ϑ

Δ is the winding hot-spot temperature rise above the ambient temperature at the

considered load

Note that the ambient temperature may not be independent of the loading, but may be a

function of the loading :

=a

This function may vary from one site to another Knowledge of this correlation for the

particular site is necessary to make relevant estimates of the ageing rate and consumption of

lifetime The correlation may be found by measurement at the specific site If no such

information is available, indications regarding ageing rate and lifetime consumption can be

obtained by making alternative calculations at different ambient temperatures, for example

within the range 10 °C to 40 °C

The formulas given in this standard consider eddy losses as ohmic losses in the windings

Test data indicates that the formulas show higher loss of lifetime than expected If harmonic

currents are present, the increased eddy losses during overloading may need additional

consideration in accordance with Annex A of IEC 61378-1

The normal lifetime of a transformer is in practice at least 180 000 h In order to express the

ageing rate k as consumption of lifetime-hours per hour of operation time at a temperature T

in Kelvins (K), 180 000 h is used as a conservative reference in the following equation:

)exp(

000

T

b a

The relative ageing rate kr at constant hot-spot temperature T, in Kelvins (K), expressed as a

percentage of the ageing rate that gives 180 000 h lifetime is calculated according to the

equation:

)exp(

T

b a

t

a and b are be to taken from Table 1

The lifetime consumptionL , expressed in hours (h), at a constant hot-spot temperature T, in c

Kelvins (K), during a time t in hours (h) is calculated according to the equation:

)exp(

t

a and b are taken from Table 1

5.6 Hot-spot temperature in steady state

For most transformers in service, the hot-spot temperature inside a winding is not precisely

known For most of these units, the hot-spot temperature can be assessed by calculation

The calculation rules in this document are based on the following:

ϑ is the hot-spot temperature, in degrees Celsius (°C), at rated conditions (rated current,

rated ambient temperature, rated voltage, rated frequency…)

The parameter ϑHScan be found by calculation method or by test

NOTE Although there is no standard test to determine the hot-spot temperature, if the manufacturer demonstrates

other values by test, the manufacturer can use these values to carry out calculation of the life consumption of the

transformer

5.7 Assumed hot-spot factor

For the following consideration, the assumed hot-spot factor Z is 1,25:

Wr r

Δ is average winding temperature rise at rated load, in Kelvin (K)

5.8 Hot-spot temperature rises at varying ambient temperature and load conditions

The basic value required for calculating the life consumption is the temperature at the

hot-spot For this purpose, it is necessary to know the temperature rise at this position for each

load condition as well as the ambient temperature

q n Wr HSn =Z ×Δ ×I

I is the loading factor per unit;

q is equal to 1,6 for air natural cooling (AN) ; or

is equal to 2 for AF cooled transformers (AF);

Z is assumed to be 1,25

Whenever possible it is preferable to use test results for ΔϑWr, to limit the uncertainty

regarding the validity of the factor Z and the value of q Experience shows that q and Z

assume different values depending on the type of transformer and the level of the load current

The hot-spot temperature ϑHS as a function of load for steady-state conditions should be

calculated by the following equations:

HS a

For AN cooling the following equation applies:

[ ]I 2m

r HS,

HS ϑ

ϑ =Δ

r HS, k

HS k T

ϑ

ϑ+

ϑ is the rated or tested hot-spot temperature at 1,0 per unit load, in degrees Celsius

(°C) [tested values for self-cooled operation for use in Equation (11) may be different

than tested values for fan-cooled operation for use in Equation (12)] ;

I is loading factor per unit (ratio between load current and rated current);

T

C is the temperature correction for resistance change with temperature;

m is an empirical constant, which is equal to 0,8 (suggested unless test data is

X is an empirical constant used in forced-air calculation, which is 1 (suggested unless

test data available)

Test data indicates that the above equations should result in conservative predictions of the

hot-spot temperature

The m exponent of 0,8 for self-cooled operation and the X exponent of 1 for forced-air

operation are derived from heat transfer correlation for natural and forced convection Test

data indicates that a temperature correction for resistance given by Equation (13) is required

to predict hot-spot temperatures rise during forced-air loading due to the higher losses

present at forced-cooled operation

Equation (11) and Equation (12) ignore eddy losses in the windings, which vary inversely with

temperature The formula provides a conservative result since Eddy losses are usually low

unless harmonic currents are present

Equation (11) and Equation (12) require an iterative calculation procedure Using the

suggested exponents and considering the resistance change with temperature for fan-cooled

operation should result in conservative calculations of the hot-spot temperature rise, even

when eddy losses are ignored If harmonic currents are present, the increased eddy losses

during overloading may need consideration in accordance with Annex A of IEC 61378-1

5.9.2 Transient loading

The hot-spot temperature rise due to transient overloading should be determined by the

following equations:

i i

−Δ

=Δ

−t

(14)

a t

Δ is the ultimate hot-spot temperature rise in Kelvins (K) if the per unit overload I U

continued until the hot-spot temperature rise stabilised;

t is the time, in minutes (min);

R

τ is the time constant in minutes (min) for the transformer at rated load;

τ is the time constant in minutes (min) for the transformer at a given load;

HS

ϑ is the hot-spot temperature in degrees Celsius (°C);

a

ϑ is the ambient temperature in degrees Celsius (°C)

5.10 Determination of winding time constant

5.10.1 General

The concept of a transformer time constant is based on the assumption that a single heat

source supplies heat to a single heat sink and that the temperature rise of the sink is an

exponential function of the heat input The time constant is defined as the time for the

temperature rise over ambient to change 63,2 % after a step change in load Typically the

temperature stabilises after 5 time constants Hot-spot temperature calculations for loading

should be made on both the low-voltage and high-voltage windings since published test data

indicates that the time constants may be different Insulation system temperature classes for

the two windings may also be different

The time constant should be calculated or determined by test on the transformer after

agreement between supplier and purchaser

5.10.2 Time constant calculation method

The time constant of a winding at rated load, τR, is:

r

e r HS, R

P

where

C is the effective thermal capacity of winding, in watt-minutes per K (Wmin/K),

= (15,0 × mass of aluminium conductor in kilograms (kg)) + (24,5 × mass of epoxy and

other winding insulation in kilograms (kg)), or

= (6,42 × mass of copper conductor in kilograms (kg)) + (24,5 × mass of epoxy and other

winding insulation in kilograms (kg));

or

C is the effective thermal capacity of winding, in watt-hours per K (Wh/K),

= (0,25 × mass of aluminium conductor in kilograms (kg)) + (0,408 × mass of epoxy and

other winding insulation in kilograms (kg)), or

= (0,107 × mass of copper conductor in kilograms (kg)) + (0,408 × mass of epoxy and

other winding insulation in kilograms (kg));

r

P is the winding total losses (resistive losses + eddy losses) at rated load and rated

temperature rise, in watts (W);

ϑ is the core contribution to winding hot-spot temperature rise at no load This value

should be the value given below or the value measured by the manufacturer during the

temperature rise test on the transformer

= 5 K for outer winding (usually HV)

= 25 K for inner winding (usually LV less than 1 kV)

NOTE 1 The core contribution values above are based on manufacturers’ experience

NOTE 2 Other winding insulation material and kind of epoxy material can be used For such transformers the

correspondent specific heat values of 24,5 Wmin/K and /kg (or 0,408 Wh/K and per kg) can be replaced by the

values based on the manufacturer’s experience

5.10.3 Time constant test method

Time constants may also be estimated from the hot resistance cooling curve obtained during

thermal tests

5.11 Determination of winding time constant according to empirical constant

When the temperature rise changes, the time constant varies according to the empirical

constant m

r

e r HS, R

)(

P

If m is equal to 1, Equation (17) is correct for any load and any starting temperature If m is

not equal to 1, the time constant for any load and for any starting temperature for either a

heating cycle or a cooling cycle is given by Equation (18)

m m

1

r HS, i 1

r HS, U

r HS,

i r

HS, U R

Δ

=

ϑ

ϑϑ

ϑ

ϑ

ϑϑ

ϑτ

5.12 Calculation of loading capability

Equations (10) through (18) should be used to determine hot-spot temperatures during a load

cycle They should also be used to determine the short-time or continuous loading, which

results in the maximum temperatures given in Table 1 or any other limiting temperatures

The initial hot-spot temperature rise for the initial loading factor Ii should be obtained from

Equation (11) and is determined as follows:

[ ]Ii 2m

r HS,

i ϑ

ϑ =Δ

where

I is the initial loading factor (ratio between load current and rated current)

From Table 2, select the limiting hot-spot temperatureϑHS For the ambient temperature,

determine the permissible hot-spot temperature rise at time t from Equation (10)

Table 2 – Maximum hot-spot winding temperature

Insulation system temperature

Calculation of the lifetime is not practical for hot-spot temperature over the maximum hot-spot

winding temperature indicated in the Table 2 because the winding material composition may

change Transformer loading that results in temperatures that exceed the limits in Table 2

risks transformer failures in an unpredictably short period of time

a HS

Δ is the hot-spot temperature rise in Kelvin (K) at time t after changing the load

Determine the ultimate hot-spot temperature rise from Equation (14)

i i

t U

)exp(

τ

ϑϑ

=Δ

where

U

ϑ

Δ is the ultimate hot spot temperature rise in Kelvin (K)

The time constant τ should be obtained from 5.9 Select a time t for the duration of the load

cycle to substitute in the above equation From Equation (11) the overload corresponding to

these conditions may be obtained as follows:

1

r HS,

U U

Δ

=ϑ

where

U

I is the ultimate loading factor

The determination of the time constant should be done by an iteration process

6 Limitations

6.1 Current and temperature limitations

With loading values beyond the nameplate rating, the hot-spot winding temperature shown in

Table 3 shall not be exceeded and the specific limitations given in 4.3 and 5.12 shall be taken

into account

The current magnitude is limited to 1,5 I especially when the cycle is short and repeated to r

avoid mechanical damage in the winding Values over 1,5 I shall be specified at the enquiry r

stage and shall be agreed upon between purchaser and manufacturer For all other types of

cycles the current is limited to 1,5 I r

Table 3 – Current and temperature limits applicable to loading

beyond nameplate rating

Insulation system temperature (°C) 105

(A)

120 (E)

130 (B)

155 (F)

180 (H)

200 220 Maximum current (p.u.) 1,5 1,5 1,5 1,5 1,5 1,5 1,5

Highest temperature for hot-spot (°C) 130 145 155 180 205 225 245

NOTE 1 The temperature and current limits are not intended to be valid simultaneously The current may be

limited to a lower value than shown in order to meet the temperature limitation requirement Conversely, the

temperature may be limited to a lower value than shown in order to meet the current limitation requirement

NOTE 2 The calculation shows that at the highest hot-spot temperature shown in the table the lifetime of a

new transformer is only few thousand hours

6.2 Other limitations

6.2.1 Magnetic leakage field in structural metallic parts

The magnetic leakage field increases with increasing current This field may cause excessive

temperatures in structural metallic parts that may restrict the overloading The limits on load

current, hot-spot temperature and temperature of structural metallic parts other than windings

and leads stated in Table 2 should not be exceeded It should be noted that when the hot-spot

temperature exceeds the highest temperature in Table 2 according to the insulation classes of

the transformer, the characteristics of the insulation system decrease to a level below the

minimum value for the dielectric withstand of the transformer

6.2.2 Accessories and other considerations

Aside from the windings, other parts of the transformer, such as bushings, cable-end

connections, tap-changing devices, tap changer, temperature measurement devices, surge

arresters and leads may restrict the operation at 1,5 times the rated current

6.2.3 Transformers in an enclosure

Consumption of life time due to overload is higher when the transformer is in an enclosure

When transformers are used indoors, a correction should be made to the rated hot-spot

temperature rise to account for the enclosure

6.2.4 Outdoor ambient conditions

In many parts of the world, direct sunshine may increase the transformer temperature

drastically, which should be taken into account when loading beyond rated current is

considered

Wind may improve the cooling of the transformer, but its unpredictable nature makes it

impractical to take into account FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU LICENSED TO MECON Limited - RANCHI/BANGALORE

Annex A (informative) Ageing rate

A.1 Loading capability

The loading capability of transformers is related to properties of the insulating materials and

insulation systems While the dominant solid insulating materials of oil-immersed transformers

are cellulose products, a larger variety of different insulating materials are used in dry-type

transformers

A.2 Molecule structure

A.2.1 General

One common feature of the solid insulating materials is the molecule structure, which consists

of long chains of smaller molecules linked together The chains may contain branches,

hexagonal rings and cross-links between chains

Figure A.1 shows an example of such a molecule structure of an epoxy

IEC 2001/08

Figure A.1 – Molecule structure of an epoxy

The molecules move In a solid material, these movements have the character of oscillations

When heat due to the losses in the winding conductor (or other sources of heat) is transferred

to the insulation material, the heat energy is converted to kinetic energy in the material Due

to the increased kinetic energy, the movements of the molecules become faster and with

larger amplitudes, in other words, more violent The probability that molecules break into

smaller molecules when they collide with each other increases This kind of chemical process

where heat is supplied to the material is called an endothermic process

A.2.2 Oxidation

Other mechanisms may occur, such as oxidation

The rate of this chemical reaction is temperature dependent, which in turn depends on the

amount of heat transferred to the insulation material

Insulation materials are developed to achieve optimum properties for their application The

change in the material molecular structure during the endothermic process causes also

changes in important properties of the material, like mechanical and dielectric strength,

thermal shock resistance and sealing performance Usually a decline in these properties takes

place The decline in different properties may not happen at the same rate The word ageing

is commonly used for this chemical process and the consequential decline in the various

material properties

A.2.3 Thermal endurance properties

A.2.3.1 General

Thermal index (TI) and the halving interval (HIC) are two terms used to characterise the

thermal endurance properties of an insulating material or system TI is the numerical value of

the temperature in degrees Celsius derived from the thermal endurance relationship at a

certain time In relevant IEC standards this time is 20 000 h, but other times can in principle

also be specified HIC is the numerical value of the temperature interval in Kelvins, which

expresses the halving of the chosen time to end-point taken at the temperature equal to TI

See Figure A.2

TI and HIC are found experimentally in accelerated tests at elevated temperatures, and the

method is based on the validity of Arrhenius’ equation

The chemist and physicist Svante Arrhenius (winner of the Nobel price in chemistry 1903)

launched the following general correlation between temperature and chemical reaction rate:

Ea is the activation energy related to the specific material;

R is the universal gas constant;

T is the temperature in Kelvins (K); and

e is the base number of the natural logarithm system (2,718 28…)

Equation (A.1) is known as Arrhenius’ equation or Arrhenius’ law

R has the value of 8,314 × 10–3 kJ mol–1K–1 The activation energy Ea is the amount of energy

needed for a reaction to happen to the specific material under consideration, and it is

assumed that Ea does not vary with the temperature Ea has the unit kJ mol–1

A and k have basically the unit second–1 (s–1), but other time units can also be used when

suitable, for example hour k indicates how rapidly the chemical reaction in the material or in

the combination of materials proceeds

The inverse of (A.1) becomes:

T R

E

e A k

(A.2)

The unit of 1/k is the second (s), and it indicates the time elapsed to the chemical reaction has

proceeded to a certain stage

Equation (A.2) can also be written:

T

b

e a

where

A.2.3.3 Thermal endurance graph

When corresponding values of ln h and 1/T are plotted in a Cartesian diagram, the points will

be situated on a straight line Such a graph is called a thermal endurance graph An example

is shown in Figure A.2

The experiments are made at higher temperatures than the expected temperature of the

temperature index (TI) In the example in Figure A.2 the experiments are made at four

different temperatures, 170 ºC, 160 ºC, 150 ºC and 140 ºC

In the experiments an end-point of the material property under investigation (for example the

a.c breakdown voltage) must be defined The end-point may be defined as a minimum

absolute value (e.g in kV/mm) or a percentual remaining value of the property before the

experiment started Such end-points are suggested in IEC standards for some materials and

properties but not for all IEC 60216-2 contains some suggestions for a number of material

properties In other cases the definition of end-points may be subject to agreement between

supplier and purchaser of the material

An end-point defined as for example 50 % remaining value could be perceived as ‘end of life’

for the insulation However, this should not be taken too literally Definition of end-points in

IEC is mainly conventional and is not functional The deterioration of the material happens

gradually The end-point represents no sharp limit between ‘life’ and ‘death’ of the

transformer Reaching the end-point means only that the particular material property has been

reduced to a certain percentage of its original value, and that the safety margins and

consequently the service reliability of the transformer have been reduced in relation to a new

transformer With respect to for example dielectric properties, the transformer may still

perform well for many years if no serious over voltages occur

Likewise, if no high over currents occur due to short-circuits in the power system, the

transformer may operate well in spite of degraded mechanical properties

In Figure A.2 the four dots indicate the time in hours needed to reach the defined end-point at

the four different temperatures 170 ºC, 160 ºC, 150 ºC and 140 °C according to the thermal

endurance test A regression line is drawn between the four points and extended to intersect

the 20 000 h ordinate The intersection takes place at a temperature of 130 °C

Consequently the material TI for this particular property is 130 Further the regression line

shows that the estimated temperature increase that would bring the material to the endpoint

after 10 000 h is about 5 ºC The halving interval HIC is then 5

0,002 30 0,002 35

0,002 40 0,002 45

0,002 50 0,002 55

Y-axis: time (logarithmic scale) in hours (h)

X-axis: reciprocal thermodynamic temperature (linear scale) in Kelvins (K –1 )

additional temperature axis: Celsius temperature (°C) (nonlinear scale)

estimated temperature at 20 000 h

estimated temperature at 10 000 h

TI thermal index

HIC halving interval

Figure A.2 – Thermal endurance graph

Because different material properties may decline at different rates, it may be necessary to

assign several temperature indexes and halving intervals to one and the same material

Detailed descriptions regarding the experimental procedures are given in IEC 60216-1 to

IEC 60216-6 Figure A.2 shows a simplified and idealised picture that just demonstrates the

principle In reality there will be dispersion in the results from the material samples, partly due

to real variations in the material, partly due to measurement uncertainty

Detailed instructions for calculating thermal endurance characteristics from large bodies of

experimental data are provided in IEC 60216-3, including statistical test to verify the validity

of using Arrhenius’ law Materials containing substantial quantities of inorganic components

may deviate considerably from Arrhenius’ law

This loading guide is based on Arrhenius’ law

The temperature within a transformer winding varies Certain areas in a winding are exposed

to higher temperatures than others The material deterioration rate is highest in high

temperature areas These areas will reach the end-point first and determine the service

reliability of the whole transformer

The relation between the hot-spot temperature and the average temperature in the windings

may vary from one design to another The formulas for the hot-spot temperature are general

and may imply an uncertainty that makes the prediction of lifetime consumption

correspondingly uncertain Manufacturers may be able to provide more precise information on

hot-spot temperatures for their particular design

When assessing the load capability of a transformer, the ambient temperature as a function of

the load must be taken into consideration

A.3 Reference documents

IEC 60216-1, Electrical insulating materials – Properties of thermal endurance –

Part 1: Ageing procedures and evaluation of test results

IEC 60216-2, Electrical insulating materials – Thermal endurance properties –

Part 2: Determination of thermal endurance properties of electrical insulating materials –

Choice of test criteria

IEC 60216-3, Electrical insulating materials – Thermal endurance properties –

Part 3: Instructions for calculating thermal endurance characteristics

IEC 60216-4-1, Electrical insulating materials – Thermal endurance properties –

Part 4-1: Ageing ovens – Single-chamber ovens

IEC 60216-4-2, Electrical insulating materials – Thermal endurance properties –

Part 4-2: Ageing ovens – Precision ovens for use up to 300 °C

IEC 60216-4-3, Electrical insulating materials – Thermal endurance properties –

Part 4-3: Ageing ovens – Multi-chamber ovens

IEC 60216-5, Electrical insulating materials – Thermal endurance properties –

Part 5: Determination of relative thermal endurance index (RTE) of an insulating material

IEC 60216-6, Electrical insulating materials – Thermal endurance properties –

Part 6: Determination of thermal endurance indices (TI and RTE) of an insulating material

using the fixed time frame method

Annex B (informative) Examples of lifetime consumptions for 3 load regimes

B.1 Example 1: Loading at constant temperature

B.1.1 Assumptions

Hot-spot temperature rise above ambient: 125 K

Ambient temperature: 30 °C = constant

Insulation system temperature: 130 °C (B)

Which means 43,48 h lifetime consumption per hour

With a loading time of 168 h, the consumption of lifetime in the course of one week at this

temperature becomes:

43,48 × 168 = 7 305 lifetime hours

The expected lifetime at the rated hot-spot temperature, 120 °C, is 180 000 h One week at a

hot-spot temperature 155 °C consumes then:

100 × 7 305 / 180 000 = 4,06 %

of the total expected lifetime of the transformer

B.2 Example 2: Loading current Ii for a time t1 followed by loading current Iu

for a time t2

B.2.1 General

When the load current suddenly changes from one level I1 to another I2 the hot-spot winding

temperature is assumed to change from an initial temperature rise Δϑ1 to an Δϑ2 according

to the exponential function (Equation 14) as shown in figure below

Δϑ u

IuT

Y-axis Upper curve: initial and ultimate loading

Lower curve: temperature rise above ambient temperature

Figure B.1 – Step change loading curve B.2.2 Assumptions

Rated time constant for the considered winding: τr = 0,5 h

Ambient temperature: 30 °C constant (independent of the load current)

Insulation system temperature: 155 °C

The hot-spot spot winding temperature at time = 0 is ΔϑHSi

The average winding temperature rise at rated current ΔϑWr= 80 K

Self-cooled operation

B.2.3 Calculation

Equation (9) is used to calculate ΔϑHSi and ΔϑHSu :

HSiϑ

Δ = 1,25 × 80 × 0,81,6 = 70 K

HSuϑ

Δ = 1,25 × 80 × 1,21,6 = 134 K

r HS,ϑ

Δ = 1,25 × 80 = 100 K

Equation (18) is used to calculate the time constant for the change in the hot-spot winding

temperature rise from 70 K to 134 K:

100

70 100

134

100

70 100 134

Equation (14) is used to calculate the momentary value of ΔϑHS at any time t in the time

interval when ΔϑHS changes from ΔϑHSi to ΔϑHSu :

HSuϑ

Δ = 70 + (134 – 70) × (1 – exp (–t / 0,399))

The ageing rate increases continuously as ΔϑHS increases See Figure B.2

HSϑ

Δ ≈ ΔϑHSu when t ≈ 5 × τ = 5 × 0,399 = 1,995 h, say 2 h

In order to calculate the lifetime consumption during the transition interval between ΔϑHSi and

HSu

ϑ

Δ simultaneous values of time, hot-spot temperature rise ΔϑHS, thermodynamic

temperature T and ageing rate k are listed in Table B.1 for the time interval t – t1 = 0 to 2 h

Table B.1 – Lifetime consumption calculations

Time temperature Hot-spot

rise

Thermodynamic temperature

Ageing rate consumption Lifetime

Time temperature Hot-spot

rise Thermodynamic temperature

Ageing rate consumption Lifetime

X-axis: time after t1 in hours (h)

Y-axis: Left hot-spot temperature rise in Kelvin (K)

Right lifetime consumption rate k in hours per hour (h/h)

Upper red curve: hot-spot temperature rise in Kelvin (K)

Lower blue curve: lifetime consumption rate corresponding to the hot - spot temperature rise

Figure B.2 – Hot-spot temperature rise and life consumption

The lifetime consumption for the 2 h long period of transition from ΔϑHSi to ΔϑHSu is

represented by the area below the lower solid curve There are several ways to estimate this

area A simple way is to draw a horizontal straight line across the diagram The line shall be

situated at an ordinate that makes the size of the two areas A1 and A2 equal judged by the

eye The boundaries of the area A1 are the left ordinate axis, the horizontal line and the solid

curve The boundaries of the area A2 are the right ordinate axis, the horizontal line and the

solid curve The ordinate on the right axis is read, and the area below the curve for k is equal

to the product of this ordinate and the time at the right end of the X-axis In this case:

5,0 × 2 = 10 (h)

This means that the lifetime consumption during the 2 h long time interval while the hot-spot

temperature rise increases from 70 K to 134 K is 10 h

In addition to these hours comes the lifetime consumption due to 10 h at 70 K hot-spot

temperature rise and 10 – 2 = 8 h at 134 K The two latter contributions can be calculated by

Equation (7)

Lc1= 180 000 × 10 × (9,60 E – 17)–1× exp(–20 475 /(273+100)) = 0,03 h

Lc2 = 180 000 × 8 × (9,60 E – 17)–1× exp(–20 475 /(273+164)) = 67,28 h

They are 0,03 h and 67,28 h respectively

The total lifetime consumption during the total 20 h considered is then:

0,03 + 9,71 + 67,28 = 77,02 h

Other ways to determine the area below the curve for k in the transition interval are the

numerical integration methods, the rectangular, trapezoidal or Simpson’s rule

The k-curve has a shape that can be described by a polynomial, which is easy to integrate to

obtain the size of the area below the curve By this method, the lifetime is 8,54 h if the step of

calculation is 0,01 h

B.3 Example 3: Varying load current

B.3.1 Assumptions

Loading current varying between 0,7 p.u and 1,2 p.u during a 24 h period

Rated time constant for the considered winding: τr = 0,5 h

Ambient temperature: 30 °C constant (independent of the loading current)

Insulation system temperature: 180 °C

The average winding temperature rise at rated current ΔϑWr = 100 K

Self-cooled operation

B.3.2 Calculation

The load cycle is shown in the two left columns of Table B.2 and in Figure B.3 The load

current is recorded once every hour

In order to calculate the lifetime consumption during 24 h period simultaneous values of time,

hot-spot temperature rise ΔϑHS, thermodynamic temperature T and ageing rate k are listed in

Table B.2

Table B.2 – Life consumption calculations for varying load

Time constant

Hot spot tempera- ture rise

Thermodynamic temperature Ageing rate k Time

sump- tion of life

Notice that there is some variation in the time constant during the cycle

X-axis time in hours (h)

Y-axis left: load current (p.u.)

Y-axis right: winding hot-spot temperature rise in Kelvin (K)

Blue curve load current, corresponding to left Y-axis (p.u.) and corresponding to symbol Ii

Red curve winding hot-spot temperature rise, corresponding to right Y-axis (K)

Figure B.3 – Load current and winding hot-spot temperature rise

The curve in Figure B.4 shows how the ageing rate varies with the time during the 24 h cycle

The lifetime consumption in the course of the cycle is the area below this curve

X-axis time in hours (h)

Y-axis ageing rate in hours per hour (h/h)

Figure B.4 – Ageing rate versus time

The area below the curve can be found by means of Simpson’s rule of numerical integration,

which says:

y y y y n

a b dt t

6)(

where 2n is the number of equal subdivision intervals in the total interval from a to b

In the present example 2n = 24 (n = 12), and the ordinatesy ,0 y , 1 y etc., are the values of k, 2

b = 24 and a = 0

The following table can be set up:

Table B.3 – Life consumption calculation

The area of below the curve in Figure B.4 is then:

78 , 53 34 , 161 12 6

24

=

×

This means that during the given 24 h loading cycle 53,78 lifetime hours is consumed of a

total lifetime of 180 000 h, which is 0,029 9 % of the total lifetime

Annex C (informative) List of symbols

C effective thermal capacity of winding

W•min/

K

or W•h/K

k ageing rate as consumption of lifetime-hours per hour of operation time at a temperature h/h 5.4

kr

relative ageing rate at constant hot-spot temperature T

(in Kelvin) expressed as a percentage of the ageing rate

P winding total losses (resistive losses+ eddy losses) at

q empirical constant for calculation of hot-spot temperature rise at a considered load 5.8

Ti insulation system temperature (thermal index Ti) °C 5.2

k

T temperature constant for conductor, which is 225 for

X empirical constant used in forced-air calculation , which is 1 (suggested unless test data available) 5.9.1

HS,

ϑ winding rated hot-spot temperature calculated or tested hot-spot temperature at 1,0 per unit °C 5.9.1 5.2

Symbol Meaning Units Subclause

Δ winding hot-spot temperature rise above the ambient temperature at the considered load

hot-spot temperature rise at the considered load K

5.2 5.8

ultimate hot-spot temperature rise if the per unit

overload I continued until the hot-spot temperature rise U

stabilized ultimate hot-spot temperature rise

K 5.9.2 5.12

r

W

ϑ

Δ average winding temperature rise at rated load K 5.7

τ time constant for the transformer at a given load min 5.9.2

τ R time constant for the transformer at rated load min 5.9.2

Bibliography

IEC 60076-1, Power transformers – Part 1: General

IEC 60076-2, Power transformers – Part 2: Temperature rise

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